TSTP Solution File: LAT289+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT289+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:43 EDT 2022
% Result : Theorem 6.29s 4.23s
% Output : Proof 6.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT289+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 13:17:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 6.29/4.23 % SZS status Theorem
% 6.29/4.23 % SZS output start Proof
% 6.29/4.23 tff(r2_hidden_type, type, (
% 6.29/4.23 r2_hidden: ( $i * $i ) > $o)).
% 6.29/4.23 tff(k8_funct_2_type, type, (
% 6.29/4.23 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 6.29/4.23 tff(tptp_fun_B_1_type, type, (
% 6.29/4.23 tptp_fun_B_1: $i)).
% 6.29/4.23 tff(k9_lopclset_type, type, (
% 6.29/4.23 k9_lopclset: $i > $i)).
% 6.29/4.23 tff(tptp_fun_A_0_type, type, (
% 6.29/4.23 tptp_fun_A_0: $i)).
% 6.29/4.23 tff(k1_zfmisc_1_type, type, (
% 6.29/4.23 k1_zfmisc_1: $i > $i)).
% 6.29/4.23 tff(k7_lopclset_type, type, (
% 6.29/4.23 k7_lopclset: $i > $i)).
% 6.29/4.23 tff(u1_struct_0_type, type, (
% 6.29/4.23 u1_struct_0: $i > $i)).
% 6.29/4.23 tff(tptp_fun_C_2_type, type, (
% 6.29/4.23 tptp_fun_C_2: $i)).
% 6.29/4.23 tff(k1_funct_1_type, type, (
% 6.29/4.23 k1_funct_1: ( $i * $i ) > $i)).
% 6.29/4.23 tff(k8_lopclset_type, type, (
% 6.29/4.23 k8_lopclset: $i > $i)).
% 6.29/4.23 tff(v17_lattices_type, type, (
% 6.29/4.23 v17_lattices: $i > $o)).
% 6.29/4.23 tff(v10_lattices_type, type, (
% 6.29/4.23 v10_lattices: $i > $o)).
% 6.29/4.23 tff(l3_lattices_type, type, (
% 6.29/4.23 l3_lattices: $i > $o)).
% 6.29/4.23 tff(v3_struct_0_type, type, (
% 6.29/4.23 v3_struct_0: $i > $o)).
% 6.29/4.23 tff(v3_realset2_type, type, (
% 6.29/4.23 v3_realset2: $i > $o)).
% 6.29/4.23 tff(v1_filter_0_type, type, (
% 6.29/4.23 v1_filter_0: ( $i * $i ) > $o)).
% 6.29/4.23 tff(m1_filter_0_type, type, (
% 6.29/4.23 m1_filter_0: ( $i * $i ) > $o)).
% 6.29/4.23 tff(m1_subset_1_type, type, (
% 6.29/4.23 m1_subset_1: ( $i * $i ) > $o)).
% 6.29/4.23 tff(v1_xboole_0_type, type, (
% 6.29/4.23 v1_xboole_0: $i > $o)).
% 6.29/4.23 tff(l1_struct_0_type, type, (
% 6.29/4.23 l1_struct_0: $i > $o)).
% 6.29/4.23 tff(l2_lattices_type, type, (
% 6.29/4.23 l2_lattices: $i > $o)).
% 6.29/4.23 tff(l1_lattices_type, type, (
% 6.29/4.23 l1_lattices: $i > $o)).
% 6.29/4.23 tff(v1_funct_1_type, type, (
% 6.29/4.23 v1_funct_1: $i > $o)).
% 6.29/4.23 tff(m2_relset_1_type, type, (
% 6.29/4.23 m2_relset_1: ( $i * $i * $i ) > $o)).
% 6.29/4.23 tff(v1_funct_2_type, type, (
% 6.29/4.23 v1_funct_2: ( $i * $i * $i ) > $o)).
% 6.29/4.23 tff(m1_relset_1_type, type, (
% 6.29/4.23 m1_relset_1: ( $i * $i * $i ) > $o)).
% 6.29/4.23 tff(1,plain,
% 6.29/4.23 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(2,plain,
% 6.29/4.23 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[1])).
% 6.29/4.23 tff(3,plain,
% 6.29/4.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(4,plain,
% 6.29/4.23 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[3])).
% 6.29/4.23 tff(5,plain,
% 6.29/4.23 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(6,plain,
% 6.29/4.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(7,plain,
% 6.29/4.23 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[6])).
% 6.29/4.23 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k9_lopclset')).
% 6.29/4.23 tff(9,plain,
% 6.29/4.23 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[8, 7])).
% 6.29/4.23 tff(10,plain,
% 6.29/4.23 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[9, 5])).
% 6.29/4.23 tff(11,plain,(
% 6.29/4.23 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 6.29/4.23 inference(skolemize,[status(sab)],[10])).
% 6.29/4.23 tff(12,plain,
% 6.29/4.23 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[11, 4])).
% 6.29/4.23 tff(13,plain,
% 6.29/4.23 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[12, 2])).
% 6.29/4.23 tff(14,plain,
% 6.29/4.23 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(15,plain,
% 6.29/4.23 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(16,plain,
% 6.29/4.23 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(17,plain,
% 6.29/4.23 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)))))))),
% 6.29/4.23 inference(monotonicity,[status(thm)],[16, 15])).
% 6.29/4.23 tff(18,plain,
% 6.29/4.23 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))),
% 6.29/4.23 inference(transitivity,[status(thm)],[17, 14])).
% 6.29/4.23 tff(19,plain,
% 6.29/4.23 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C)))))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(20,plain,
% 6.29/4.23 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (~((v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)))) & r2_hidden(B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C)))))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(21,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (~((v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)))) & r2_hidden(B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t27_lopclset')).
% 6.29/4.23 tff(22,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[21, 20])).
% 6.29/4.23 tff(23,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[22, 19])).
% 6.29/4.23 tff(24,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[23, 19])).
% 6.29/4.23 tff(25,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[24, 19])).
% 6.29/4.23 tff(26,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[25, 19])).
% 6.29/4.23 tff(27,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[26, 19])).
% 6.29/4.23 tff(28,plain,
% 6.29/4.23 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[27, 19])).
% 6.29/4.23 tff(29,plain,
% 6.29/4.23 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[28, 18])).
% 6.29/4.23 tff(30,plain,
% 6.29/4.23 (l3_lattices(A!0)),
% 6.29/4.23 inference(and_elim,[status(thm)],[29])).
% 6.29/4.23 tff(31,plain,
% 6.29/4.23 (~v3_realset2(A!0)),
% 6.29/4.23 inference(and_elim,[status(thm)],[29])).
% 6.29/4.23 tff(32,plain,
% 6.29/4.23 (v17_lattices(A!0)),
% 6.29/4.23 inference(and_elim,[status(thm)],[29])).
% 6.29/4.23 tff(33,plain,
% 6.29/4.23 (v10_lattices(A!0)),
% 6.29/4.23 inference(and_elim,[status(thm)],[29])).
% 6.29/4.23 tff(34,plain,
% 6.29/4.23 (~v3_struct_0(A!0)),
% 6.29/4.23 inference(and_elim,[status(thm)],[29])).
% 6.29/4.23 tff(35,plain,
% 6.29/4.23 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(36,plain,
% 6.29/4.23 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(37,plain,
% 6.29/4.23 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0))))),
% 6.29/4.23 inference(monotonicity,[status(thm)],[36])).
% 6.29/4.23 tff(38,plain,
% 6.29/4.23 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 6.29/4.23 inference(transitivity,[status(thm)],[37, 35])).
% 6.29/4.23 tff(39,plain,
% 6.29/4.23 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 6.29/4.23 inference(quant_inst,[status(thm)],[])).
% 6.29/4.23 tff(40,plain,
% 6.29/4.23 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[39, 38])).
% 6.29/4.23 tff(41,plain,
% 6.29/4.23 (k9_lopclset(A!0) = k8_lopclset(A!0)),
% 6.29/4.23 inference(unit_resolution,[status(thm)],[40, 34, 33, 32, 31, 30, 13])).
% 6.29/4.23 tff(42,plain,
% 6.29/4.23 (k8_lopclset(A!0) = k9_lopclset(A!0)),
% 6.29/4.23 inference(symmetry,[status(thm)],[41])).
% 6.29/4.23 tff(43,plain,
% 6.29/4.23 (k1_funct_1(k8_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)),
% 6.29/4.23 inference(monotonicity,[status(thm)],[42])).
% 6.29/4.23 tff(44,plain,
% 6.29/4.23 (k1_funct_1(k9_lopclset(A!0), B!1) = k1_funct_1(k8_lopclset(A!0), B!1)),
% 6.29/4.23 inference(symmetry,[status(thm)],[43])).
% 6.29/4.23 tff(45,plain,
% 6.29/4.23 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(46,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[45])).
% 6.29/4.23 tff(47,plain,
% 6.29/4.23 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(48,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[47])).
% 6.29/4.23 tff(49,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(50,plain,
% 6.29/4.23 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(51,plain,
% 6.29/4.23 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[50])).
% 6.29/4.23 tff(52,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 6.29/4.23 tff(53,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[52, 51])).
% 6.29/4.23 tff(54,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[53, 49])).
% 6.29/4.23 tff(55,plain,(
% 6.29/4.23 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.29/4.23 inference(skolemize,[status(sab)],[54])).
% 6.29/4.23 tff(56,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[55, 48])).
% 6.29/4.23 tff(57,plain,
% 6.29/4.23 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[56, 46])).
% 6.29/4.23 tff(58,plain,
% 6.29/4.23 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(59,plain,
% 6.29/4.23 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 6.29/4.23 inference(quant_inst,[status(thm)],[])).
% 6.29/4.23 tff(60,plain,
% 6.29/4.23 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[59, 58])).
% 6.29/4.23 tff(61,plain,
% 6.29/4.23 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 6.29/4.23 inference(unit_resolution,[status(thm)],[60, 30, 57])).
% 6.29/4.23 tff(62,plain,
% 6.29/4.23 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 6.29/4.23 inference(tautology,[status(thm)],[])).
% 6.29/4.23 tff(63,plain,
% 6.29/4.23 (l2_lattices(A!0)),
% 6.29/4.23 inference(unit_resolution,[status(thm)],[62, 61])).
% 6.29/4.23 tff(64,plain,
% 6.29/4.23 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(65,plain,
% 6.29/4.23 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[64])).
% 6.29/4.23 tff(66,plain,
% 6.29/4.23 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(67,plain,
% 6.29/4.23 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(68,plain,
% 6.29/4.23 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[67])).
% 6.29/4.23 tff(69,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 6.29/4.23 tff(70,plain,
% 6.29/4.23 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[69, 68])).
% 6.29/4.23 tff(71,plain,
% 6.29/4.23 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[70, 66])).
% 6.29/4.23 tff(72,plain,(
% 6.29/4.23 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(skolemize,[status(sab)],[71])).
% 6.29/4.23 tff(73,plain,
% 6.29/4.23 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[72, 65])).
% 6.29/4.23 tff(74,plain,
% 6.29/4.23 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(75,plain,
% 6.29/4.23 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 6.29/4.23 inference(quant_inst,[status(thm)],[])).
% 6.29/4.23 tff(76,plain,
% 6.29/4.23 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 6.29/4.23 inference(modus_ponens,[status(thm)],[75, 74])).
% 6.29/4.23 tff(77,plain,
% 6.29/4.23 (l1_struct_0(A!0)),
% 6.29/4.23 inference(unit_resolution,[status(thm)],[76, 73, 63])).
% 6.29/4.23 tff(78,plain,
% 6.29/4.23 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(79,plain,
% 6.29/4.23 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[78])).
% 6.29/4.23 tff(80,plain,
% 6.29/4.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(81,plain,
% 6.29/4.23 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.29/4.23 inference(quant_intro,[status(thm)],[80])).
% 6.29/4.23 tff(82,plain,
% 6.29/4.23 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.29/4.23 inference(rewrite,[status(thm)],[])).
% 6.29/4.23 tff(83,plain,
% 6.29/4.23 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 6.29/4.23 inference(bind,[status(th)],[])).
% 6.29/4.23 tff(84,plain,
% 6.29/4.23 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[83])).
% 6.29/4.24 tff(85,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 6.29/4.24 tff(86,plain,
% 6.29/4.24 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[85, 84])).
% 6.29/4.24 tff(87,plain,
% 6.29/4.24 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[86, 82])).
% 6.29/4.24 tff(88,plain,(
% 6.29/4.24 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.29/4.24 inference(skolemize,[status(sab)],[87])).
% 6.29/4.24 tff(89,plain,
% 6.29/4.24 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[88, 81])).
% 6.29/4.24 tff(90,plain,
% 6.29/4.24 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[89, 79])).
% 6.29/4.24 tff(91,plain,
% 6.29/4.24 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(92,plain,
% 6.29/4.24 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(93,plain,
% 6.29/4.24 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 6.29/4.24 inference(monotonicity,[status(thm)],[92])).
% 6.29/4.24 tff(94,plain,
% 6.29/4.24 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.29/4.24 inference(transitivity,[status(thm)],[93, 91])).
% 6.29/4.24 tff(95,plain,
% 6.29/4.24 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 6.29/4.24 inference(quant_inst,[status(thm)],[])).
% 6.29/4.24 tff(96,plain,
% 6.29/4.24 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[95, 94])).
% 6.29/4.24 tff(97,plain,
% 6.29/4.24 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[96, 34, 90])).
% 6.29/4.24 tff(98,plain,
% 6.29/4.24 (~v1_xboole_0(u1_struct_0(A!0))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[97, 77])).
% 6.29/4.24 tff(99,plain,
% 6.29/4.24 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(100,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[99])).
% 6.29/4.24 tff(101,plain,
% 6.29/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) <=> (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(102,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[101])).
% 6.29/4.24 tff(103,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(104,plain,
% 6.29/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), rewrite(((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) <=> (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(105,plain,
% 6.29/4.24 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[104])).
% 6.29/4.24 tff(106,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k9_lopclset')).
% 6.29/4.24 tff(107,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[106, 105])).
% 6.29/4.24 tff(108,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[107, 103])).
% 6.29/4.24 tff(109,plain,(
% 6.29/4.24 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 6.29/4.24 inference(skolemize,[status(sab)],[108])).
% 6.29/4.24 tff(110,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[109, 102])).
% 6.29/4.24 tff(111,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[110, 100])).
% 6.29/4.24 tff(112,plain,
% 6.29/4.24 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(113,plain,
% 6.29/4.24 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))),
% 6.29/4.24 inference(quant_inst,[status(thm)],[])).
% 6.29/4.24 tff(114,plain,
% 6.29/4.24 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[113, 112])).
% 6.29/4.24 tff(115,plain,
% 6.29/4.24 (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[114, 34, 33, 32, 31, 30, 111])).
% 6.29/4.24 tff(116,plain,
% 6.29/4.24 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | v1_funct_1(k9_lopclset(A!0))),
% 6.29/4.24 inference(tautology,[status(thm)],[])).
% 6.29/4.24 tff(117,plain,
% 6.29/4.24 (v1_funct_1(k9_lopclset(A!0))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[116, 115])).
% 6.29/4.24 tff(118,plain,
% 6.29/4.24 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(tautology,[status(thm)],[])).
% 6.29/4.24 tff(119,plain,
% 6.29/4.24 (v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[118, 115])).
% 6.29/4.24 tff(120,plain,
% 6.29/4.24 (m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(monotonicity,[status(thm)],[42])).
% 6.29/4.24 tff(121,plain,
% 6.29/4.24 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(122,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[121])).
% 6.29/4.24 tff(123,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(124,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 6.29/4.24 tff(125,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[124, 123])).
% 6.29/4.24 tff(126,plain,(
% 6.29/4.24 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 6.29/4.24 inference(skolemize,[status(sab)],[125])).
% 6.29/4.24 tff(127,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[126, 122])).
% 6.29/4.24 tff(128,plain,
% 6.29/4.24 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 6.29/4.24 inference(quant_inst,[status(thm)],[])).
% 6.29/4.24 tff(129,plain,
% 6.29/4.24 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[128, 127])).
% 6.29/4.24 tff(130,plain,
% 6.29/4.24 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(monotonicity,[status(thm)],[42])).
% 6.29/4.24 tff(131,plain,
% 6.29/4.24 (m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(symmetry,[status(thm)],[130])).
% 6.29/4.24 tff(132,plain,
% 6.29/4.24 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(tautology,[status(thm)],[])).
% 6.29/4.24 tff(133,plain,
% 6.29/4.24 (m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[132, 115])).
% 6.29/4.24 tff(134,plain,
% 6.29/4.24 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[133, 131])).
% 6.29/4.24 tff(135,plain,
% 6.29/4.24 ((~(m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | (~m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(tautology,[status(thm)],[])).
% 6.29/4.24 tff(136,plain,
% 6.29/4.24 (m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[135, 134, 129])).
% 6.29/4.24 tff(137,plain,
% 6.29/4.24 (m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[136, 120])).
% 6.29/4.24 tff(138,plain,
% 6.29/4.24 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(139,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[138])).
% 6.29/4.24 tff(140,plain,
% 6.29/4.24 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(141,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[140])).
% 6.29/4.24 tff(142,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(143,plain,
% 6.29/4.24 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(144,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[143])).
% 6.29/4.24 tff(145,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 6.29/4.24 tff(146,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[145, 144])).
% 6.29/4.24 tff(147,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[146, 142])).
% 6.29/4.24 tff(148,plain,(
% 6.29/4.24 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 6.29/4.24 inference(skolemize,[status(sab)],[147])).
% 6.29/4.24 tff(149,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[148, 141])).
% 6.29/4.24 tff(150,plain,
% 6.29/4.24 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[149, 139])).
% 6.29/4.24 tff(151,plain,
% 6.29/4.24 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 6.29/4.24 inference(and_elim,[status(thm)],[29])).
% 6.29/4.24 tff(152,plain,
% 6.29/4.24 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(153,plain,
% 6.29/4.24 (((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(154,plain,
% 6.29/4.24 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))))),
% 6.29/4.24 inference(monotonicity,[status(thm)],[153])).
% 6.29/4.24 tff(155,plain,
% 6.29/4.24 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 6.29/4.24 inference(transitivity,[status(thm)],[154, 152])).
% 6.29/4.24 tff(156,plain,
% 6.29/4.24 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 6.29/4.24 inference(quant_inst,[status(thm)],[])).
% 6.29/4.24 tff(157,plain,
% 6.29/4.24 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[156, 155])).
% 6.29/4.24 tff(158,plain,
% 6.29/4.24 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[157, 151, 150])).
% 6.29/4.24 tff(159,plain,
% 6.29/4.24 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)),
% 6.29/4.24 inference(unit_resolution,[status(thm)],[158, 137, 119, 117, 98])).
% 6.29/4.24 tff(160,plain,
% 6.29/4.24 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k8_lopclset(A!0), B!1)),
% 6.29/4.24 inference(transitivity,[status(thm)],[159, 44])).
% 6.29/4.24 tff(161,plain,
% 6.29/4.24 (r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1)) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 6.29/4.24 inference(monotonicity,[status(thm)],[160])).
% 6.29/4.24 tff(162,plain,
% 6.29/4.24 (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 6.29/4.24 inference(symmetry,[status(thm)],[161])).
% 6.29/4.24 tff(163,plain,
% 6.29/4.24 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(164,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[163])).
% 6.29/4.24 tff(165,plain,
% 6.29/4.24 (^[A: $i] : rewrite((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(166,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[165])).
% 6.29/4.24 tff(167,plain,
% 6.29/4.24 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.24 inference(transitivity,[status(thm)],[166, 164])).
% 6.29/4.24 tff(168,plain,
% 6.29/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A)))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(169,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[168])).
% 6.29/4.24 tff(170,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 6.29/4.24 inference(rewrite,[status(thm)],[])).
% 6.29/4.24 tff(171,plain,
% 6.29/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))) <=> ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), (![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))) <=> ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))))),
% 6.29/4.24 inference(bind,[status(th)],[])).
% 6.29/4.24 tff(172,plain,
% 6.29/4.24 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 6.29/4.24 inference(quant_intro,[status(thm)],[171])).
% 6.29/4.24 tff(173,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_lopclset')).
% 6.29/4.24 tff(174,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[173, 172])).
% 6.29/4.24 tff(175,plain,
% 6.29/4.24 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 6.29/4.24 inference(modus_ponens,[status(thm)],[174, 170])).
% 6.29/4.24 tff(176,plain,(
% 6.29/4.24 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 6.29/4.25 inference(skolemize,[status(sab)],[175])).
% 6.29/4.25 tff(177,plain,
% 6.29/4.25 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.25 inference(modus_ponens,[status(thm)],[176, 169])).
% 6.29/4.25 tff(178,plain,
% 6.29/4.25 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))),
% 6.29/4.25 inference(modus_ponens,[status(thm)],[177, 167])).
% 6.29/4.25 tff(179,plain,
% 6.29/4.25 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))))))))),
% 6.29/4.25 inference(rewrite,[status(thm)],[])).
% 6.29/4.25 tff(180,plain,
% 6.29/4.25 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))))))))),
% 6.29/4.25 inference(quant_inst,[status(thm)],[])).
% 6.29/4.25 tff(181,plain,
% 6.29/4.25 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A))))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))),
% 6.29/4.25 inference(modus_ponens,[status(thm)],[180, 179])).
% 6.29/4.25 tff(182,plain,
% 6.29/4.25 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))),
% 6.29/4.25 inference(unit_resolution,[status(thm)],[181, 34, 33, 32, 31, 30, 178])).
% 6.29/4.25 tff(183,plain,
% 6.29/4.25 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0)))))))),
% 6.29/4.25 inference(rewrite,[status(thm)],[])).
% 6.29/4.25 tff(184,plain,
% 6.29/4.25 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0)))))))),
% 6.29/4.25 inference(quant_inst,[status(thm)],[])).
% 6.29/4.25 tff(185,plain,
% 6.29/4.25 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)) <=> (~((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))),
% 6.29/4.25 inference(modus_ponens,[status(thm)],[184, 183])).
% 6.29/4.25 tff(186,plain,
% 6.29/4.25 (![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))),
% 6.29/4.25 inference(unit_resolution,[status(thm)],[185, 151, 182])).
% 6.29/4.25 tff(187,plain,
% 6.29/4.25 (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))),
% 6.29/4.25 inference(and_elim,[status(thm)],[29])).
% 6.29/4.25 tff(188,plain,
% 6.29/4.25 (m1_filter_0(C!2, A!0)),
% 6.29/4.25 inference(or_elim,[status(thm)],[187])).
% 6.29/4.25 tff(189,plain,
% 6.29/4.25 (((~![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))) | ((~m1_filter_0(C!2, A!0)) | (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))))))) <=> ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))) | (~m1_filter_0(C!2, A!0)) | (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))))))),
% 6.29/4.25 inference(rewrite,[status(thm)],[])).
% 6.29/4.25 tff(190,plain,
% 6.29/4.25 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))) | ((~m1_filter_0(C!2, A!0)) | (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))))))),
% 6.29/4.25 inference(quant_inst,[status(thm)],[])).
% 6.29/4.25 tff(191,plain,
% 6.29/4.25 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))))))) | (~m1_filter_0(C!2, A!0)) | (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))))),
% 6.29/4.25 inference(modus_ponens,[status(thm)],[190, 189])).
% 6.29/4.25 tff(192,plain,
% 6.29/4.25 (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))))),
% 6.29/4.25 inference(unit_resolution,[status(thm)],[191, 188, 186])).
% 6.29/4.25 tff(193,plain,
% 6.29/4.25 (v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)),
% 6.29/4.25 inference(or_elim,[status(thm)],[187])).
% 6.29/4.25 tff(194,plain,
% 6.29/4.25 (r2_hidden(B!1, C!2)),
% 6.29/4.25 inference(and_elim,[status(thm)],[193])).
% 6.29/4.25 tff(195,plain,
% 6.29/4.25 (v1_filter_0(C!2, A!0)),
% 6.29/4.25 inference(and_elim,[status(thm)],[193])).
% 6.29/4.25 tff(196,plain,
% 6.29/4.25 ((~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))) | (~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))),
% 6.29/4.28 inference(tautology,[status(thm)],[])).
% 6.29/4.28 tff(197,plain,
% 6.29/4.28 (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))),
% 6.29/4.28 inference(unit_resolution,[status(thm)],[196, 195, 194])).
% 6.29/4.28 tff(198,plain,
% 6.29/4.28 ((~(r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))))) | r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) | ((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))),
% 6.29/4.28 inference(tautology,[status(thm)],[])).
% 6.29/4.28 tff(199,plain,
% 6.29/4.28 ((~(r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))))) | r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 6.29/4.28 inference(unit_resolution,[status(thm)],[198, 197])).
% 6.29/4.28 tff(200,plain,
% 6.29/4.28 (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 6.29/4.28 inference(unit_resolution,[status(thm)],[199, 192])).
% 6.29/4.28 tff(201,plain,
% 6.29/4.28 (r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 6.29/4.28 inference(modus_ponens,[status(thm)],[200, 162])).
% 6.29/4.28 tff(202,plain,
% 6.29/4.28 (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 6.29/4.28 inference(and_elim,[status(thm)],[193])).
% 6.29/4.28 tff(203,plain,
% 6.29/4.28 ($false),
% 6.29/4.28 inference(unit_resolution,[status(thm)],[202, 201])).
% 6.29/4.28 % SZS output end Proof
%------------------------------------------------------------------------------